Comparison of Five Design Variables of Response Surface Designs in a Spherical Region Over a Set of Reduced Models

Abstract

The research extended the work of Chomtee and Borkowski (2012) which compared response surface designs—central composite designs (CCDs), Box-Behnken designs (BBDs), small composite designs (SCDs), Plackett-Burman composite designs (PBDs) and uniform shell designs (USDs)—over a set of reduced models in a spherical design region for five design variables (k = 5) based on the three alphabetic optimality criteria—D and G where larger values imply a better design (on a per point basis) and IV (where a smaller value implies a better design). The results present a comparison of the design optimality criteria of the response surface designs across the full second order model and a set of reduced models (839 models) for five factors based on the three alphabetic optimality criteria. The results of the comparison ranking of the D, G and IV criteria of reduced models showed that for small design sizes, N = 23, 25, 27 and 29, based on D and G, the SCD (n0 = 1, 3) are recommended over the PBD (n0 = 1, 3). For medium design sizes, N = 31, 33 and 35, based on D and G, the USD (n0 = 1, 3) are recommended over the PBD (rs = 2, n0 = 1, 3), and when N = 35, 37, the SCD (rs = 2, n0 = 1) is recommended over the PBD (rs = 2, n0 = 3). For a large design size, N = 43, based on D, the CCD (n0 = 1) is recommended over the BBD (n0 = 3), and based on G and IV, the BBD (n0 = 3) is recommended over the CCD (n0 = 1).